Proposition All S Are P
every member of the s class is a member of the p class, that is, the s class is included in the p class
Proposition No S are P
No member of the s class is a member of the P class, that is, the s class is excluded from the p class
Some S are P
At least one member of the S class is a member of the P class
Some S are not P
At least one member of the S class is not a member of the P class
What is the quality of a categorical proposition?
quality means it is either affirmative or negative depending on whether it affirms or denies class membership.
no s are p and some s are not p
negative quality
all s are p and some s are p
affirmative quality
Qualities in propositions
called affirmative propositions and negative propositions.
Quantity
in a categorical proposition, the quantity is either universal or particular depending on whether the statement makes a claim about every member or just some member of the class denoted by the subject term.
All S are P" "No S are P" quantity
Universal propositions
Some s are p, and some s are not p
particular propositions because they assert something about one or more members of the s class
How to determine the quantity of a categorical proposition
through mere inspection of the quantifier. All and no immediately imply universal quantity, while some implies particular
A proposition
universal affirmative, all s are p
e proposition
universal negative, no s are p
i proposition
particular affirmative, some s are p
O proposition
particular negative som s are not p
Universal
A, E
Particular
I, O
Proposition All S are P
A, quantity universal, quality affirmative
proposition no s are p
E, quantity universal, quality negative
proposition some s are p
I, quantity particular, quality affirmative
some s are not p
O, quantity particular, quality negative.
Some
particular
all or no
universal
Distribution
attribute of the terms (subject and predicate) of propositions
Unprepared Students Never Pass
Universals distribute subjects. Negative sDistribut Predicates
Any student earning b's is not on probation
A distributes Subject. Edistributes Both. I distributes neither, O distributes Predicate
All S Are P
A, universal, affirmative, terms distributed S.
No S are P
E, universal, negative, Terms distributed s and p
Some s are p
I, particular, affirmative, terms distributed none.
Some S are not P
O, particular, negative, terms distributed, P
No vampire movies are films without blood
Categorical proposition E, (No are. Universal quantity, negative quality, Subject and Predicatedistributed (vampire moves
All governments that bargain with terrorists are governments that encourage terrorism
categorical proposition A, Universal quantity, affirmative quality, Subject distributed
some symphony orchestras are organizations on the brink of bankruptcy
I, particular quantity, affirmative quality, no terms distributed
some chinese leaders are not thoroughgoing opponents of capitalist economics
O, particular quantity, negative quality, predicate distributed
all human contacts with benzene are potential causes of cancer
A, universal quantity, affirmative quality, subject distributed
no labor strikes are events welcomed by management
E. universal quantity, negative quality, subject and predicate distributed
some hospitals are organizations that overcharge the medicare program
I. particular quantity, affirmative quality, no terms distributed
some affirmative action plans are not programs that result in reverse discrimination
O, particular quantity, negative quality, predicate distributed.
existential import
means that in a proposition, at least one or more things denoted by the subject term actually exist.
Conversion
Switch subject and predicate terms
obversion
change the quality; replace predicate with term complement
contraposition
switch subject and predicate terms, replace each with it's term complement
E and I propositions are
logically equivalent when they necessarily have the same truth value
steps to obversion
1) change the quality (no s are p to all s are p and vice versa.
2) change the term to the term complement (book to non-book, animal to non-animal)
overs of All A are B
No A are non-b
obverse of no a are b
all a are non- b
overse of some a are b
some a are not non b
some a are not b
some a are non- b
contraposition steps
1) switching the subject and predicate terms 2)replacing the subject and predicate terms with their term complements
contrapose "All goats are animals
all non animals are non goats
Convert No A are Non B (T)
No non b are A Undetermined
Some A are B (T) Contraposition
Some Non b are not Non a (truth)
Switch subject and predicate terms; Replace each with it's term complement
contraposition. A and O propositions can have same truth value as given statement. E and i will yield an undetermined truth value. You cannot contra pose E and I propositions
No A are B > No B are A
conversion same truth value as given statement
All a are b > all b are a
conversion , a proposition undetermined truth value when converted
some a are b > some be are a
conversion same truth statement
some a are not b > some b are not a
undetermined truth statement, conversion
obverse of All A are B
No B are a (same truth value as given statement)
obverse of No a are b
all a are non- b
obverse of some a are b
some a are not non-b
obverse of some a are not b
some a are non-b